I can so relate. When I was renting it was so hard to find a place to allow dogs, I had to pay a huge security deposit and a monthly pet fee, AND a cleaning fee before moving out, it stunk majorly bad. And even the crappiest apartments wouldn't allow a small dog, it was just insanity.
I always say call ALL the apts in the newspaper.. you'd be surprised that some people will allow it if you really explain the situation. I know having a training certificate can help in a lot of situations. I got probably 70 nos before I got one yes, so just keep trying!!